Many modern circuits are provided in the form of integrated circuits. Integrated circuit fabrication enables components to be formed at high density and with degrees of component matching which is extremely difficult to achieve in discrete components without resorting to trimming. As a consequence integrated circuits can achieve high precision by exploiting the relative values of various components, thereby overcoming the problem that absolute values within integrated circuits may vary considerably (in the order of 10% or more) from one wafer lot to another.
The matching between components is often exploited to produce high precision or high resolution circuits. For example analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) having resolution of 12 to 16 bits are available due to the ability to match components within an integrated circuit. Circuit design techniques, such as segmentation, can be used to make circuits less sensitive to inter-component variation and to allow circuits to achieve, for example, 16 bit precision without needing components to be matched to 16 bit accuracy.
However, in use, current flow in a component within an integrated circuit can cause local heating of a component which can cause it to vary in value compared to similar components.
To put this into perspective consider a 16 bit DAC. Suppose that a resistor representing the most significant bit has a value X and a first order temperature coefficient dX/dT of 50×10−6 (50 ppm). This first order temperature coefficient is realistic as it is known to a person skilled in the art that thin film resistors typically exhibit temperature coefficients of less than 100 parts per million.
If heating of the resistor due to current flow through the resistor caused its temperature to change by 2° C. then the value of the resistor changes by a factor of 100×10−6. Although this change sounds relatively small, it should be compared to the least significant bit size within, for example, a 16 bit DAC.
The LSB of a 16 bit DAC corresponds to a value of (2−16−1)=1.526×10−5 of the DAC output range. Therefore the self-heating of a resistor which constitutes the most significant bit resistor could, in this example, give rise to an error of 100×10−6÷1.526×10−5=6.5 LSB. Thus a relatively modest temperature of only 2° C. could give rise to an error in the range of 6 to 7 least significant bits (LSBs).
The self-heating also affects transistors. For example in a bipolar junction transistor the emitter current IE can be approximated by the Ebers-Moll model:IE=IESexp((VBE/VT)−1)Where VT=kT/q, IES is the reverse saturation current of the emitter-base junction, VBE is the base-emitter voltage, k is Boltzmann's constant, T is the temperature in Kelvin and q is the charge of an electron.
The temperature dependent factor within the exponential term gives rise to a real threat of current change through the transistor as a result of self-heating which might be important in differential amplifiers, comparators and current mirrors having high current multiplication ratios.